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Analysis of a temporal discretization for a semilinear fractional diffusion equation
Computers & Mathematics with Applications ( IF 2.9 ) Pub Date : 2020-09-25 , DOI: 10.1016/j.camwa.2020.09.008
Binjie Li , Tao Wang , Xiaoping Xie

This paper considers a temporal discretization of a semilinear fractional diffusion equation with nonsmooth initial data. With appropriately graded temporal grids, first-order temporal accuracy in the norm of L2(0,T;L2(Ω)) is derived by a new discrete Grönwall’s inequality, and then first-order temporal accuracy in the norm of L(0,T;L2(Ω)) is established for 12<α<1. Finally, numerical results are provided to verify the theoretical results.



中文翻译:

半线性分数扩散方程的时间离散化分析

本文考虑具有不光滑初始数据的半线性分数扩散方程的时间离散化。使用适当分级的时间网格,范数范数的一阶时间精度大号20Ť;大号2Ω 由一个新的离散Grönwall不等式推导得出,然后由 大号0Ť;大号2Ω1个2<α<1个。最后,提供数值结果以验证理论结果。

更新日期:2020-09-26
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